Question

How do you verify `tan^5 x = tan ^3 x sec^2 x - tan^3 x`?

Answer 1

`RHS=tan^3x*sec^2x-tan^3x`

`=tan^3x(sec^2x-1)=tan^3x*tan^2x=tan^5x=LHS`

Answer 2

`"see explanation"`

Explanation:

`"using the "color(blue)"trigonometric identity"`

`•color(white)(x)1+tan^2x=sec^2x`

`"consider the left side"`

`tan^5x=tan^3x xxtan^2x`

`color(white)(tan^5x)=tan^3x(sec^2x-1)`

`color(white)(tan^5x)=tan^3xsec^2x-tan^3x=" right side"`